Trying to solve the Poschl-Teller potential (quantum mechanics)(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

I have a superpotential that give me 2 of the Poschl-Teller potentials.

The superpotential is:

W(x)=-b*cot(x)

The Poschl-Teller potentials are:

J(x,b)=b(b-1)/(sin(x))^2-b^2

K(x,b)=b(b+1)/(sin(x))^2-b^2

2. Relevant equations

Schrodinger equation: Hψ=Eψ

3. The attempt at a solution

I placed the potential in Schrodinger equation (neglecting the existence of constants) and received the following equations:

ψ''(x)+(2E-J)ψ(x)=0

ψ''(x)+(2E-K)ψ(x)=0

I do not know what the next step I should do

I know I need to get to Legendre polynomial but I don't know how...

Can anyone show me how to do it?

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# Trying to solve the Poschl-Teller potential

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